Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-11T07:03:56.916Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability of ice lenses in saline soils

Published online by Cambridge University Press:  14 January 2020

S. S. L. Peppin Open the ORCID record for S. S. L. Peppin [Opens in a new window]
S. S. L. Peppin*
Affiliation:
Mississauga, L5G 2K5, Canada
*
†Email address for correspondence: speppin@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

A model of the growth of an ice lens in a saline porous medium is developed. At high lens growth rates the pore fluid becomes supercooled relative to its equilibrium Clapeyron temperature. Instability occurs when the supercooling increases with distance away from the ice lens. Solute diffusion in the pore fluid significantly enhances the instability. An expression for the segregation potential of the soil is obtained from the condition for marginal stability of the ice lens. The model is applied to a clayey silt and a glass powder medium, indicating parameter regimes where the ice lens stability is controlled by viscous flow or by solute diffusion. A mushy layer, composed of vertical ice veins and horizontal ice lenses, forms in the soil in response to the instability. A marginal equilibrium condition is used to estimate the segregated ice fraction in the mushy layer as a function of the freezing rate and salinity.

JFM classification

Convection: Convection in porous media Phase change: Solidification/melting Phase change: Morphological instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 886 , 10 March 2020 , A16
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Acker, J. P., Elliott, J. A. W. & McGann, L. E. 2001 Intercellular ice propagation: experimental evidence for ice growth through membrane pores. Biophys. J. 81 (3), 1389–1397.CrossRefGoogle ScholarPubMed
Anderson, A. M. & Worster, M. G. 2012 Periodic ice banding in freezing colloidal dispersions. Langmuir 28, 16512–16523.CrossRefGoogle ScholarPubMed
Anderson, A. M. & Worster, M. G. 2014 Freezing colloidal suspensions: periodic ice lenses and compaction. J. Fluid Mech. 758, 786–808.CrossRefGoogle Scholar
Arenson, L. U., Azmatch, T. F. & Sego, D. C. 2008 A new hypothesis on ice lens formation in frost-susceptible soils. In 9th International Conference on Permafrost, pp. 59–64. Fairbanks.Google Scholar
Arenson, L. U., Xia, D., Sego, D. C. & Biggar, K. W. 2006 Change in ice lens formation for saline and non-saline Devon silt as a function of temperature and pressure. In Cold Regions Engineering 2006: Current Practices in Cold Regions Engineering, pp. 1–11. ASCE.Google Scholar
Azmatch, T. F.2013 Frost heave: new ice lens initiation condition and hydraulic conductivity prediction. PhD thesis, University of Alberta, Edmonton, Canada.Google Scholar
Bear, J. 1972 Dynamics of Fluids in Porous Media. Elsevier.Google Scholar
Bear, J. & Corapcioglu, M. Y. 1981 Mathematical model for regional land subsidence due to pumping: 1. Integrated aquifer subsidence equations based on vertical displacement only. Water Resour. Res. 17 (4), 937–946.CrossRefGoogle Scholar
Beskow, G. 1935 Soil Freezing and Frost Heaving with Special Applications to Roads and Railroads. Northwestern University: Technological Institute, reprinted in Historical Perspectives in Frost Heave Research (P. B. Black and M. J. Hardenberg, eds.) CRREL Special Report No. 91-23, pp. 37–157, 1991.Google Scholar
Bird, R. B., Stuart, W. E. & Lightfoot, E. N. 2002 Transport Phenomena, 2nd edn. Wiley.Google Scholar
Black, P.1990 Three functions that model empirically measured unfrozen water content and predict relative hydraulic conductivity. CRREL Tech. Rep. 90-5, 1–7.Google Scholar
Brown, S. C. & Payne, D. 1990 Frost action in clay soils. II. Ice and water location and suction of unfrozen water in clays below 0 °C. J. Soil Sci. 41, 547–561.CrossRefGoogle Scholar
Butler, M. F. 2001 Instability formation and directional dendritic growth of ice studied by optical interferometry. Cryst. Growth Des. 1 (3), 213–223.CrossRefGoogle Scholar
Chamberlain, E. J. 1983 Frost heave of saline soils. In Proceedings of the 4th International Conference on Permafrost, pp. 121–126. Fairbanks.Google Scholar
Chamberlain, E. J. & Gow, A. J. 1979 Effect of freezing and thawing on the permeability and structure of soils. Engng Geol. 13, 73–92.CrossRefGoogle Scholar
Coriell, S. R. & Sekerka, R. F. 1983 Oscillatory morphological instabilities due to nonequilibrium segregation. J. Cryst. Growth 61, 499–508.CrossRefGoogle Scholar
Corte, A. E. 1962 Vertical migration of particles in front of a moving freezing plane. J. Geophys. Res. 67 (3), 1085–1090.CrossRefGoogle Scholar
Dash, J. G., Rempel, A. W. & Wettlaufer, J. S. 2006 The physics of premelted ice and its geophysical consequences. Rev. Mod. Phys. 78, 695–741.CrossRefGoogle Scholar
Davis, S. H. 2001 Theory of Solidification. Cambridge University Press.CrossRefGoogle Scholar
Dedovets, D. & Deville, S. 2018 Multiphase imaging of freezing particle suspensions by confocal microscopy. J. Eur. Ceram. Soc. 38 (7), 2687–2693.CrossRefGoogle Scholar
Dedovets, D., Monteux, C. & Deville, S. 2018 Five-dimensional imaging of freezing emulsions with solute effects. Science 360 (6386), 303–306.CrossRefGoogle ScholarPubMed
Deville, S. 2013 Ice templating, freeze casting: beyond materials processing. J. Mater. Res. 28, 2202–2219.CrossRefGoogle Scholar
Deville, S. 2017 Freezing Colloids: Observations, Principles, Control, and Use. Springer International.CrossRefGoogle Scholar
Deville, S., Saiz, E., Nalla, R. K. & Tomsia, A. P. 2006 Freezing as a path to build complex composites. Science 311, 515–518.CrossRefGoogle ScholarPubMed
El Hasadi, Y. M. F. & Kodadadi, J. M. 2015 Numerical simulation of solidification of colloids inside a differentially heated cavity. J. Heat Transfer 137, 072301.CrossRefGoogle Scholar
Fowler, A. & Krantz, W. B. 1994 A generalized secondary frost heave model. SIAM J. Appl. Maths 54, 1650–1675.CrossRefGoogle Scholar
Freeze, R. A. & Cherry, J. A. 1979 Groundwater. Prentice Hall.Google Scholar
Gao, W., Smith, D. W. & Li, Y. 2006 Natural freezing as a wastewater treatment method: E. coli inactivation capacity. Water Res. 40 (12), 2321–2326.CrossRefGoogle ScholarPubMed
Gay, G. & Azouni, A. M. 2002 Forced migration of nonsoluble and soluble metallic pollutants ahead of a liquid–solid interface during unidirectional freezing of dilute clayey suspensions. Cryst. Growth Des. 2, 135–140.CrossRefGoogle Scholar
Gilpin, R. R. 1982 A frost heave interface condition for use in numerical modelling. In Engineering Applications in Permafrost Areas. Proceedings of the Fourth Canadian Permafrost Conference, pp. 459–465. National Research Council of Canada.Google Scholar
Ginot, F., Lenavetier, T., Dedovets, D. & Deville, S.2019 Solute effects in confined freezing. arXiv:1907.10502.Google Scholar
deGroot, S. R. & Mazur, P. 1962 Non-Equilibrium Thermodynamics. North-Holland Publishing Co.Google Scholar
Gross, G. W., Gutjahr, A. & Caylor, K. 1987 Recent experimental work on solute redistribution at the ice/water interface. Implications for electrical properties and interface processes. J. Phys. Colloq. 48 (C1), 527–533.Google Scholar
Hallet, B. 1978 Solute redistribution in freezing ground. In Proceedings of the 3rd International Conference on Permafrost, Edmonton, Alberta, pp. 86–91. International Permafrost Association.Google Scholar
Henderson, T. M. A., Ladewiq, K., Haylock, D. N., MacLean, K. M. & O’Connor, A. J. 2013 Cryogels for biomedical applications. J. Mater. Chem. B 1, 2682–2695.CrossRefGoogle Scholar
Hivon, E. G. & Sego, D. C. 1993 Distribution of saline permafrost in the Northwest Territories, Canada. Can. Geotech. J. 30 (3), 506–514.CrossRefGoogle Scholar
Konrad, J. M. 1987 Procedure for determining the segregation potential of freezing soils. Geotech. Test. J. 10, 51–58.Google Scholar
Konrad, J.-M. 1989a Influence of cooling rate on the temperature of ice lens formation in clayey silts. Cold Reg. Sci. Technol. 16 (1), 25–36.CrossRefGoogle Scholar
Konrad, J.-M. 1989b Physical processes during freeze-thaw cycles in clayey silts. Cold Reg. Sci. Technol. 16 (3), 291–303.CrossRefGoogle Scholar
Konrad, J.-M. 1990 Segregation potential – pressure – salinity relationships near thermal steady state for a clayey silt. Can. Geotech. J. 27 (2), 203–215.CrossRefGoogle Scholar
Konrad, J.-M. & McCammon, A. W. 1990 Solute partitioning in freezing soils. Can. Geotech. J. 27 (6), 726–736.CrossRefGoogle Scholar
Konrad, J.-M. & Morgenstern, N. R. 1980 A mechanistic theory of ice lens formation in fine-grained soils. Can. Geotech. J. 17 (4), 473–486.CrossRefGoogle Scholar
Konrad, J. M. & Morgenstern, N. R. 1981 The segregation potential of a freezing soil. Can. Geotech. J. 18, 482–491.CrossRefGoogle Scholar
Konrad, J.-M. & Morgenstern, N. R. 1982 Effects of applied pressure on freezing soils. Can. Geotech. J. 19 (4), 494–505.CrossRefGoogle Scholar
Konrad, J.-M. & Morgenstern, N. R. 1984 Frost heave prediction of chilled pipelines buried in unfrozen soils. Can. Geotech. J. 21 (1), 100–115.CrossRefGoogle Scholar
Körber, C. 1988 Phenomena at the advancing ice–liquid interface: solutes, particles and biological cells. Q. Rev. Biophys. 21 (2), 229–298.CrossRefGoogle ScholarPubMed
Kuroda, T. 1987 Role of water layer at an ice surface in the kinetic processes of growth of ice crystals – growth of snow crystals and frost heaving. J. Phys. Colloq. 48 (C1), 487–493.Google Scholar
Kurz, W. & Fisher, D. J. 1998 Fundamentals of Solidification, 4th edn. Trans Tech Publications Ltd.CrossRefGoogle Scholar
Leppäranta, M. 2015 Freezing of Lakes and the Evolution of Their Ice Cover. Springer.CrossRefGoogle Scholar
Loch, J. P. G. & Miller, R. D. 1975 Tests of the concept of secondary heaving. Soil Sci. Soc. Am. Proc. 39, 1036–1041.CrossRefGoogle Scholar
Mackay, J. R. 1974 Reticulate ice veins in permafrost, Northern Canada. Can. Geotech. J. 11 (2), 230–237.CrossRefGoogle Scholar
Mackay, J. R. 1975 Reticulate ice veins in permafrost, Northern Canada: reply. Can. Geotech. J. 12, 163–165.CrossRefGoogle Scholar
Miller, R. D. 1972 Freezing and heaving of saturated and unsaturated soils. Highway Res. Rec. 393, 1–11.Google Scholar
Miller, R. D. 1978 Frost heaving in non-colloidal soils. In Proceedings of the 3rd International Conference on Permafrost, Edmonton, Alberta, pp. 708–713. International Permafrost Association.Google Scholar
Mullins, W. W. & Sekerka, R. F. 1964 Stability of a planar interface during solidification of a dilute binary alloy. J. Appl. Phys. 35, 444–451.CrossRefGoogle Scholar
O’Neill, K. 1983 The physics of mathematical frost heave models: a review. Cold Reg. Sci. Technol. 6 (3), 275–291.CrossRefGoogle Scholar
Pekor, C. M. 2014 The effect of the molecular weight of polyethylene glycol on the microstructure of freeze-cast alumina. Ceram. Int. 40, 9171–9177.CrossRefGoogle Scholar
Penner, E. 1961 Ice-grain structure and crystal orientation in an ice lens from Leda clay. Geol. Soc. Am. Bull. 72, 1575–1577.CrossRefGoogle Scholar
Penner, E. 1986 Aspects of ice lens growth in soils. Cold Reg. Sci. Technol. 13 (1), 91–100.CrossRefGoogle Scholar
Peppin, S. S. L., Aussillous, P., Huppert, H. E. & Worster, M. G. 2007 Steady-state mushy layers: experiments and theory. J. Fluid Mech. 570, 69–77.CrossRefGoogle Scholar
Peppin, S. S. L., Elliott, J. A. W. & Worster, M. G. 2006 Solidification of colloidal suspensions. J. Fluid Mech. 554, 147–166.CrossRefGoogle Scholar
Peppin, S. S. L. & Style, R. W. 2013 The physics of frost heave and ice-lens growth. Vad. Zone J. 12, 1–12.Google Scholar
Peppin, S. S. L., Wettlaufer, J. S. & Worster, M. G. 2008 Experimental verification of morphological instability in freezing aqueous colloidal suspensions. Phys. Rev. Lett. 100, 238301.CrossRefGoogle ScholarPubMed
Qian, L. & Zhang, H. 2011 Controlled freezing and freeze-drying: a versatile route for porous and micro-/nano-structured materials. J. Chem. Technol. Biotechnol. 86, 172–184.CrossRefGoogle Scholar
Rempel, A. W. 2008 A theory for ice-till interactions and sediment entrainment beneath glaciers. J. Geophys. Res. Earth Surf. 113 (F1), 1–20.Google Scholar
Rempel, A. W. 2010 Frost heave. J. Glaciol. 56, 1122–1128.CrossRefGoogle Scholar
Rempel, A. W., Wettlaufer, J. S. & Worster, M. G. 2004 Premelting dynamics in a continuum model of frost heave. J. Fluid Mech. 498, 227–244.CrossRefGoogle Scholar
Saint-Michel, B., Georgelin, M., Deville, S. & Pocheau, A. 2019 Boundary-induced inhomogeneity of particle layers in the solidification of suspensions. Phys. Rev. E 99, 052601.Google ScholarPubMed
Schollick, J. M. H.2015 Real space study of pattern formation in freezing colloidal suspensions. PhD thesis, University of Oxford, Oxford, UK.Google Scholar
Schollick, J. M. H., Style, R. W., Curran, A., Wettlaufer, J. S., Dufresne, E. R., Warren, P. B., Velikov, K. P., Dullens, R. P. A. & Aarts, D. G. A. L. 2016 Segregated ice growth in a suspension of colloidal particles. J. Phys. Chem. B 120, 3941–3949.CrossRefGoogle Scholar
Sekerka, R. F. 1968 Morphological stability. J. Cryst. Growth 3–4, 71–81.CrossRefGoogle Scholar
Spannuth, M., Mochrie, S. G. J., Peppin, S. S. L. & Wettlaufer, J. S. 2011 Particle-scale structure in frozen colloidal suspensions from small-angle x-ray scattering. Phys. Rev. E 83, 021402.Google ScholarPubMed
Style, R. W. & Peppin, S. S. L. 2012 The kinetics of ice-lens growth in porous media. J. Fluid Mech. 692, 482–498.CrossRefGoogle Scholar
Style, R. W., Peppin, S. S. L., Cocks, A. C. F. & Wettlaufer, J. S. 2011 Ice lens formation and geometrical supercooling in soils and other colloidal materials. Phys. Rev. E 84, 041402.Google ScholarPubMed
Taber, S. 1929 Frost heaving. J. Geol. 37, 428–461.Google Scholar
Thomson, E. S., Hansen-Goos, H., Wettlaufer, J. S. & Wilen, L. A. 2013 Grain boundary melting in ice. J. Chem. Phys. 138 (12), 124707.Google ScholarPubMed
Tiller, W. A., Jackson, K. A., Rutter, J. W. & Chalmers, B. 1953 The redistribution of solute atoms during the solidification of metals. Acta Metall. 1 (4), 428–437.CrossRefGoogle Scholar
Walder, J. & Hallet, B. 1986 The physical basis of frost weathering: toward a fundamental and unified perspective. Arctic Alpine Res. 18, 27–32.CrossRefGoogle Scholar
Wang, H. 2000 Theory of Linear Poroelasticity. Princeton University Press.Google Scholar
Wang, L., You, J., Wang, Z., Wang, J. & Lin, X. 2016 Interface instability modes in freezing colloidal suspensions: revealed from onset of planar instability. Sci. Rep. 6, 23358.Google ScholarPubMed
Wang, Y., Wang, D., Ma, W., Wen, Z., Chen, S. & Xu, X. 2018 Laboratory observation and analysis of frost heave progression in clay from the Qinghai-Tibet Plateau. Appl. Therm. Engng 131, 381–389.CrossRefGoogle Scholar
Watanabe, K. 2002 Relationship between growth rate and supercooling in the formation of ice lenses in a glass powder. J. Cryst. Growth 237–239, 2194–2198.CrossRefGoogle Scholar
Watanabe, K. & Mizoguchi, M. 2000 Ice configuration near a growing ice lens in a freezing porous medium consisting of micro glass particles. J. Cryst. Growth 213, 135–140.CrossRefGoogle Scholar
Watanabe, K., Mizoguchi, M., Ishizaki, T. & Fukuda, M. 1997 Experimental study on microstructure near freezing front during soil freezing. In Ground Freezing 97 (ed. Knutsson, S.), pp. 187–192. CRC Press.Google Scholar
Watanabe, K., Muto, Y. & Mizoguchi, M. 2001 Water and solute distributions near an ice lens in a glass-powder medium saturated with sodium chloride solution under unidirectional freezing. Cryst. Growth Des. 1 (3), 207–211.CrossRefGoogle Scholar
Weeks, W. F. & Lofgren, G. 1967 The effective solute distribution coefficient during the freezing of NaCl solutions. In Physics of Snow and Ice. Proceedings of the International Conference on Low Temperature Science, pp. 579–597. Institute of Low Temperature Science.Google Scholar
Wettlaufer, J. S. 2019 Surface phase transitions in ice: from fundamental interactions to applications. Phil. Trans. R. Soc. Lond. A 377, 20180261.Google ScholarPubMed
Wettlaufer, J. S. & Worster, M. G. 2006 Premelting dynamics. Annu. Rev. Fluid Mech. 38, 427–452.CrossRefGoogle Scholar
Wollkind, D. J. & Segel, L. A. 1970 A nonlinear stability analysis of the freezing of a dilute binary alloy. Phil. Trans. R. Soc. Lond. A 268, 351–380.CrossRefGoogle Scholar
Worster, M. G. 1986 Solidification of an alloy from a cooled boundary. J. Fluid Mech. 167, 481–501.CrossRefGoogle Scholar
Worster, M. G. & Wettlaufer, J. S. 1999 The fluid mechanics of premelted liquid films. In Fluid Dynamics at Interfaces, pp. 339–351. Cambridge University Press.Google Scholar
Xu, Z., Yu, H., Yan, J. & Tan, L. 2016 Solidification of suspended colloids at nonplanar interfaces. Macromol. Symp. 365, 17–31.CrossRefGoogle Scholar
You, J., Wang, J., Wang, L., Wang, Z., Lia, J. & Lin, X. 2018a In situ observation of the unstable lens growth in freezing colloidal suspensions. Colloids Surf. A 553, 681–688.CrossRefGoogle Scholar
You, J., Wang, Z. & Worster, M. G. 2018b Controls on microstructural features during solidification of colloidal suspensions. Acta Mater. 157, 288–297.CrossRefGoogle Scholar